Highest Common Factor of 562, 208, 608 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 562, 208, 608 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 562, 208, 608 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 562, 208, 608 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 562, 208, 608 is 2.

HCF(562, 208, 608) = 2

HCF of 562, 208, 608 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 562, 208, 608 is 2.

Highest Common Factor of 562,208,608 using Euclid's algorithm

Highest Common Factor of 562,208,608 is 2

Step 1: Since 562 > 208, we apply the division lemma to 562 and 208, to get

562 = 208 x 2 + 146

Step 2: Since the reminder 208 ≠ 0, we apply division lemma to 146 and 208, to get

208 = 146 x 1 + 62

Step 3: We consider the new divisor 146 and the new remainder 62, and apply the division lemma to get

146 = 62 x 2 + 22

We consider the new divisor 62 and the new remainder 22,and apply the division lemma to get

62 = 22 x 2 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 562 and 208 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(62,22) = HCF(146,62) = HCF(208,146) = HCF(562,208) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 608 > 2, we apply the division lemma to 608 and 2, to get

608 = 2 x 304 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 608 is 2

Notice that 2 = HCF(608,2) .

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Frequently Asked Questions on HCF of 562, 208, 608 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 562, 208, 608?

Answer: HCF of 562, 208, 608 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 562, 208, 608 using Euclid's Algorithm?

Answer: For arbitrary numbers 562, 208, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.